The Physics Philes, lesson 87: It’s Your Density

Today is a very exciting day, young readers. Today is a day we start a new physics topic. Goodbye, periodic motion! Hello, fluid mechanics! As usual when we start a new topic, we need to get down the basics.

Fluid mechanics, as may or may not be obvious, is the study of fluids. I usually think that fluids are the same things as liquids, but it’s not. A fluid is basically anything that flows, either a gas or a liquid. We can split fluid mechanics into two general areas. There is fluid statics, which is the study of fluid at rest in equilibrium positions (which is most of what we’ll be discussing in this chapter) and fluid dynamics, which is more complex.

Before we can really dig into fluid mechanics, there are three key concepts we need to get down: density, pressure, and buoyancy. I’ll focus on density today.

Density is the amount of mass per unit of volume. In a more or less homogenous material, we can find the density by diving mass by volume. The ratio is what is important here. Different materials can have different masses and/or volumes, but the same density. Also, a material might not have the same density all the time; it depends on environmental factors like temperature and pressure. The densest material on Earth is osmium with a density of 22,500 kilogram per cubic meter. That’s pretty dense, but only if don’t think on a cosmic scale. Weird stellar objects like neutron stars are much more dense. Those typically clock in at between 3.7 x 10^17 to 5.9 x 10^17 kilograms per cubic meter, which is between 2.6 x 10614 and 4.1 x 10^14 times more dense than the sun.

Density can further be split into two concepts. First, there is something called specific gravity. Don’t get too excited. It doesn’t actually have anything to do with gravity. It’s really just the ratio of a material’s density to the density of water. I have no idea how this got all wound up with gravity. I guess it’s just one of those things you just have to remember. The second concept is average density. This is actually what is described in the definition of density. Since density can vary with temperature, altitude, and other factors, we talk about the objects average density, rather than the density at any particular point.

Now…let’s do a problem. Specifically, let’s weigh a room full of air and find it’s mass.

Let’s say we have a room that is 4.0 m x 5.0 m x 3.0 m. The air in the room is room temperature, about 20ºC. Let’s figure out the mass and weight of the air.

For the purposes of this question, we’re going to assume that the air is the same throughout the room, so the density will be the same throughout the room. Let’s first calculate the volume of the room.

Now we can just rearrange the density equation to find the mass of the air. The density of air 1.20 kilogram per cubic meter.

Now that we know the mass, we can calculate the weight of the air

Whoa! That’s, like, a person’s weight just in air! Neat.

That’s it for today. I’ve flipped through this chapter, and I think fluid mechanics is going to be pretty cool. Next week we’ll continue learning the basics with an overview of pressure.

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